If | a |=2,| b |=3,| c |=5 and each of the angles between the vectors a and b , b and c , c and a is 60^ , then the value of | a + b + c | is

Step-by-step solution

aligned a b & =| a || b | 60^ & =(2)(3) ( 1 2 ) & =3 b c & =| b || c | 60^ & =(3)(5) ( 1 2 )= 15 2 aligned aligned a c & =| a || c | 60^ & =(2)(5) ( 1 2 ) & =5 a + b + c ^2 & = . | a ^2+ | b |^2+| c |^2+2( a b + b c + c a ) & =2^2+3^2+5^2+2 (3+ 15 2 +5 ) & =4+9+25+31 & =69 | a + b + c | & = 69 aligned